The National Assessment of Educational Progress interviewed a random sample of 1917 people 21 to 25 years old. The sample contained 840 men, of whom 775 were fully employed. Of the 1077 women 680 were fully employed. Is there sufficient evidence to support the claim that the employment levels for men compared to woman were different

The p value for this case would be:

For this case the p value is very low so we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of employment levels for men compared to woman were different

Step-by-step explanation:

Information given

represent the number of people fully employed men

represent the number of people fully employed women

sample 1 selected  

sample 2 selected  

represent the proportion estimated for male employed

represent the proportion estimated for women employed

represent the pooled estimate of p

z would represent the statistic

represent the value for the test

System of hypothesis

We want to test the claim that the employment levels for men compared to woman were different, the system of hypothesis would be:    

Null hypothesis:    

Alternative hypothesis:    

For this case the statistic is given by:

  (1)  

Where  

Replacing the info given we got:

The p value for this case would be:

For this case the p value is very low so we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of employment levels for men compared to woman were different.